Convergent Star Product Algebras on " Ax + B "
نویسنده
چکیده
The notion of convergent star product is generally understood as the data of a one parameter family {Et}t∈I ⊂ C∞(M) of function algebras on a Poisson manifold (M, { , }). On each of them one is given an associative algebra structure ⋆t which respect to which the function space Et is closed. The family of products {⋆t} should moreover define in some sense a deformation of the commutative pointwise product of functions in the direction of the Poisson structure { , }. Stable function algebras for the Weyl-Moyal product have been studied in various contexts. For instance, see:
منابع مشابه
Star Product Algebras of Test Functions
We prove that the Gelfand-Shilov spaces S α are topological algebras under the Moyal star product if and only if α ≥ β. These spaces of test functions can be used in quantum field theory on noncommutative spacetime. The star product depends continuously in their topology on the noncommutativity parameter. We also prove that the series expansion of the Moyal product is absolutely convergent in S...
متن کاملCUNTZ ’ S ax + b - SEMIGROUP C ∗ - ALGEBRA OVER N AND PRODUCT SYSTEM C ∗ - ALGEBRAS
We investigate C∗-algebras associated with row-finite topological higherrank graphs with no source, which are based on product system C∗-algebras. We prove the Cuntz-Krieger uniqueness theorem, and provide the condition of simplicity and purely infiniteness of our algebras. We give examples of non-discrete topological higher-rank graphs whose C∗-algebras contain Cuntz’s ax + b-semigroup C∗-alge...
متن کاملOn module extension Banach algebras
Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule. Then ${mathcal{S}}=A oplus X$, the $l^1$-direct sum of $A$ and $X$ becomes a module extension Banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ In this paper, we investigate biflatness and biprojectivity for these Banach algebras. We also discuss on automatic continuity of derivations on ${mathcal{S...
متن کاملDeformation Quantization Modules Ii. Hochschild Class
This paper is the continuation of [12]. We construct the Hochschild class for coherent modules over a deformation quantization algebroid on a complex Poisson manifold. We also define the convolution of Hochschild homologies, and prove that the Hochschild class of the convolution of two coherent modules is the convolution of their Hochschild classes. We study with some details the case of symple...
متن کاملDERIVATIONS OF TENSOR PRODUCT OF SIMPLE C*-ALGEBRAS
In this paper we study the properties of derivations of A B, where A and B are simple separable C*-algebras, and A B is the C*-completion of A B with respect to a C*-norm Yon A B and we will characterize the derivations of A B in terms of the derivations of A and B
متن کامل